It has previously been proposed--see German Pat. No. 883 288, to which U.S. Pat. No. 2,622,521, LARSEN, corresponds--to apply damping fluid by damping fluid metering disks which are in engagement with a damping fluid pick-up roller and which, by an axially continuous, rotatable square element, can be engaged with a subsequent damping fluid transfer roller. This arrangement does not permit individual adjustment or placement of a particular disk or roller element, selectively, in transferring engagement between the pick-up roller and the subsequent transfer roller as desired. Consequently, individual metering, in axial zones, of the quantity of damping fluid being transferred to the damping fluid transfer roller is not possible, since the individual disks or roller elements cannot be separately controlled. Further, since the individual disks, as described in this reference, are not in continuous surface contact with the transfer roller, disks do not contribute to spreading or distributing of the damping roller film on the transfer roller, and, hence, to spreading and distributing of the film on downstream roller elements forming a roller train for the damping fluid, since they are held in continuous engagement with the damping fluid pick-up roller and are moved towards the transfer roller only when damping fluid is to be transferred. The entire structure is comparatively complex since more than the customary roller elements in the damping fluid train have to be used.